West Ham needed a penalty shoot-out to see off Birkirkara and reach the third qualifying round of the UEFA Europa League.
The Premier League side were beaten 1-0 by the Maltese side on the night thanks to Fabrizio Miccoli's 15th-minute effort. James Tomkins was sent off for the London club just before half-time before Mauricio Mazzetti saw red in extra time for Birkirkara.
However, Birkirkara defender Nikola Vukanac lost his composure in the shoot-out as he blazed over the bar, allowing Diego Poyet to set up a tie for West Ham with Astra - who drew 0-0 with Inverness Caledonian Thistle to go through 1-0 on aggregate.
Inverness' Scottish rivals Aberdeen are through 5-2 on aggregate following a 2-2 draw with Rijeka, but Welsh side Newtown lost 3-1 (5-1 agg) at home to Copenhagen, whose fellow Danes Brondby are into the next round (1-0 on agg) despite a 0-0 draw with Beroe.
Debrecen were the biggest winners of the night as they crushed 10-man Skonto of Latvia 9-2. The Hungarian side posted their record European score to complete an 11-4 aggregate triumph with the aid of doubles from Ibrahim Sidibe and Tibor Tisza.
Their domestic foes Ferencvaros lost 2-0 (3-0 agg) to Zeljeznicar.
Slovan Bratislava progressed in emphatic fashion, beating UCD 5-1 (6-1 agg), while PAOK hammered Lokomotiv Zagreb 6-0 (7-2 agg), Hajduk Split eased to a 4-1 (6-4 agg) win over Koper, and Sporting Charleroi defeated Beitar Jerusalem 4-1 (9-2 agg).
Rosenborg were routine 3-0 (4-0 agg) winners over KR, Legia Warsaw won by the same margin in their tie with Botosani and Trabzonspor's 2-1 victory at Differdange saw the Turkish side safely through 3-1 on aggregate.
Vojvodina drew 1-1 with Spartaks to win 4-1 over two legs and set up a tie with Sampdoria, and Wolfsberger will play Borussia Dortmund after seeing off Shakhtyor 2-0 (3-0 agg).
Rauf Aliyev's goal in extra time saw Inter Baku past FH as they drew 2-2 on the night, winning 4-3 on aggregate, and Thun got the better of Hapoel Beer Sheva 2-1 (3-2 agg).
Omonia Nicosia's goalless stalemate with Jagiellonia Bialystok, briefly halted while home goalkeeper Constantinos Panagi replaced a lost contact lens, was enough for the Cypriots to win 1-0 on aggregate and Apollon also drew 0-0 with Trakai, winning 4-0 over two legs.
A 2-0 win at Shirak saw AIK through to the next round 4-0 on aggregate, Dinamo Minsk hammered Cherno More 4-0 (5-1 agg), Vaduz knocked out Nomme Kalju with a 2-0 (5-1 agg) triumph, Qabala overturned a 1-0 first-leg deficit to eliminate Cukaricki with a 2-0 win, Odd beat Shamrock Rovers 2-1 (4-1 agg) and Gothenburg progressed thanks to a 2-0 defeat of Slask Wroclaw (2-0 agg).
Zilina overcame Dacia 4-2 (6-3 agg), Kukesi won by the same scoreline on the night at Mladost Podgorica to win 4-3 on aggregate, Spartak Trnava cruised to a 3-1 (5-2 agg) success at Linfield, Rabotnicki were 2-0 (2-1 agg) winners over Jelgava, Kairat went through 4-2 on aggregate despite losing 2-1 to Alashkert and Stromsgodset benefited from the away goals rule after a 1-0 defeat to Mlada Boleslav levelled that tie at 2-2.
